OPTIMAL PLACEMENT OF METERS FOR POWER SYSTEM STATE ESTIMATION BY USING ARTIFICIAL INTELLEGENCE TECHNIQUES, A COMPARATIVE STUDY

Meters placements play an important role in attaining the system observability for estimating the state of the power system. This paper presents algorithms to select the best locations for installing the meters by using artificial intelligence techniques. Two algorithms have been proposed and implemented in order to avoid the circumstances arisen by random distribution of the meters. The first algorithm include optimal placement of meters by using Particle Swarm Optimization (PSO). The second algorithm utilizes the Artificial Bee Colony (ABC) to select the best allocation of meters. The proposed algorithms randomly searches the best location of meter placement based on the minimum error of state estimation. In comparison to traditional methods, PSO and ABC able to search the optimal measurement placement without having to test possible location one after another since PSO and ABC are an optimization method. The performance of the proposed algorithms are verified by applying the proposed algorithms on IEEE-14 and 30 bus standard test system. The obtained results reveal the importance of optimal selection of meter placement in accelerating the convergence the state estimation process. The capability of the proposed algorithm in determining the best estimate of the state variables accurately with a less number of iterations and less execution time than conventional method (WLS) is clarified.


Introduction
State estimation is an essential tool utilized in the real-time monitoring of the power system.It is the cornerstone of the power system security analysis.State estimation determines the optimal static state of the system (voltage magnitude and phase angle) by processing the available measurements based on an appropriate system model.A big improvements in state estimation process have been reported in the literature since the pioneer work of Schweppe [1,2].One of the challenging issues in state estimation in power systems is how to satisfy the observability conditions of the system.System observability is the status of obtaining a proper state estimate by using the available measurement units.It was found in the literature [3][4][5] that the type and location of measurements is an important factor in the robustness of the state estimator.Previously, the measurement placement selection was carried out by using trial and error method on random basis.Abbasy [6] proposed an algorithm for measurement selection problem based on redundancy identification technique.An algorithm for processing the measurements sequentially and forming an observable measurements scheme was given in [7].Das [8] proposed a simple rule-based algorithm for placing the meters in a radial distribution system.
A comprehensive survey on meter placement in power system state estimation was demonstrated in [9].Optimal location of phasor measurement unit (PMU) was presented in [10][11] by using binary integer programming.Due to their promising performance, swarm intelligence techniques are still attracting the researchers and have being applied in several fields of power system analysis [12][13][14][15][16][17].Mahari [18] applied a binary imperialistic competition algorithm in optimal placement of PMU to maintain system observability.Optimal location of PMU with limited number of channels was presented in [19].
In this paper, an efficient algorithms are proposed to select the optimal locations of meters while satisfying system observability.The proposed algorithms are utilizing swarm intelligence techniques, namely Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) technique for obtaining the optimal location.This paper is organized as follows: Section 2 reviews the traditional weighted least square method.The Particle Swarm Optimization and Artificial Bee Colony techniques are presented in section 3.In Section 4 the proposed algorithms are presented.The application of the proposed algorithms on typical test systems is presented in section 5. Finally, section 6 presents the conclusion.

Traditional WLS Technique
The vector of measured quantities are related to the state vector by the following non-linear system of equation: where: [z] : Measurement vector, , ( )-: nonlinear function of the state vector used to calculate the value of the measurement, x: system state vector (voltage magnitudes and angles), , -: the error of the measurement.
The best solution of state estimate vector x may be determined by minimizing the sum of weighted squares of residuals: where, , -, -0 1 ,is a diagonal matrix whose elements are the variances of the measurement error, [weighting factor is defined by the inverse of the measurements variances.Consequently, measurements of a higher quality have smaller variances that relates to their weights.Equation ( 2) can be represented in matrix form: The necessary conditions for a minimum is that : Where, [H(x)] 0 ( ) 1 , ( )-, - Where, , [H(x)]:the measurement Jacobian matrix of dimension (m × n), k a number of iteration, is the solution vector at iteration k, , ( )-: the gain matrix, : Updated state in k+1 iteration [20].

Swarm artificial intelligence techniques
The first technique utilized in this paper is PSO presented by Eberhart and Kennedy in 1995 as a good substitute to genetic algorithm (GA).PSO is one of the population based artificial intelligence (AI) algorithms.Each particle(individual) in the population can be considered as candidate solution.The location of each particle is symbolized by -axis site.The symbol (the velocity of -axis) represents velocity (displacement vector) while represents (the velocity of -axis) .The location and the velocity information of the individual are used in modifying the location of the individual [21].The velocity of each individual is adjusted by the following equation: where is present velocity of individual i at iteration k, and are random numbers between 0 and 1, is present site of individual i at iteration k, is of individual i, is of the group, is weight function for speed of individual i, generally, the variation of the value of is assumed to be linear from 0.9 to 0.4 as the iterative process continues.is weight constants for cognitive and neighboring term.Typically, the weighting function is used in following equation: (10) where is the initial weight, is final weight, is maximum iteration number, is present iteration number.By using equation ( 10), diversification characteristics is progressively reduced.By using equation ( 9), a specific velocity that progressively obtains close to pbests and gbest can be calculated.The present site (searching point in the solution space) can be adjusted by the following equation [22]: (11) The second technique utilized in this paper is the artificial bee colony(ABC) which is introduced by Karaboga in 2005.ABC simulates the foraging demeanor of the bee colony and employs this intelligent foraging demeanor to solve numerical and engineering design optimization problems.This algorithm uses a particular communication method to find the food sources, where the food sources could be flower patch, etc.In ABC, the food sources represent the possible solutions not individuals (honey bees), where as in other algorithms, such as PSO, each possible solution represents an individual of the swarm.This feature represents an important and basic difference between the ABC and other population based on the swarm intelligence algorithms [23].
In ABC algorithm, the artificial bee colony comprises of three groups of bees: employed bees, scouts and onlookers.The first half of the colony comprises the employed bees and the second half contains the onlookers.There is only one employed bee for each food source; which means that the number of food sources around the hive is equal to the number of employed bees.The employed bee of which its food source has been deserted by the bees will become a scout [24].
The dancing area represents the most important part of the hive with respect to exchange of information, where the communication occurs among bees associated to the quality of food sources.There is a bigger chance for onlookers for selecting more profitable sources where more information is circulating about the more profitable sources.Employed foragers exchange their information with a probability, which is relative to the profitability of the food source, and the exchanging of this information through waggle dancing is longer in period.Therefore, the staffing is relative to profitability of a food source.
The followings are the main procedures of the algorithm [25]: 1.The employed bees are moved on their food sources and the quantities of nectar are determined.2. The scouts are moved to find new food sources.3. The best food source found so far is saved.
The location of a food source represents a potential solution to the optimization problem and the nectar quantity of a food source corresponds to the value (fitness) of the related solution [26].
Primary food sources are produced randomly within the domain of parameters, which could be produced by the following equation: where * + , * + , is the number of food sources, is the number of optimization parameters.and are lowers and upper boundaries of dimension, respectively.The employed bee produces an adjustment on the food source site (solution) in her memory depending on the local information (visual information) and discovers the adjacent food source and then assess its quality.To find the adjacent food source, the following equation is used: Within the neighborhood of each food source location represented by , a food source is specified by changing one parameter of .In equation ( 13), j is a random integer in the range [1,2,…D] and k {1,2,...SN} is a randomly selected indicator that has to be different from i.
is a real random number distributed uniformly in the range [-1, 1].As can be seen from equation (13), as the difference between the parameters of the and decreases, the disturbance on the site decreases.Thus, as the search approaches to the optimal solution in the search space, the procedure length is adaptively reduced.
After producing within the boundaries, a fitness value for a minimization problem can be allocated to the solution by the following equation: where is the cost value of the solution .For maximization problems, the cost function can be used directly as a fitness function.A greedy choice is applied between and ; then the best one is chosen depending on the fitness values that represents the quantity of nectar from the food sources at and .If the source at is superior to that of in terms of profitability, the employed bee saves the new site and forgets the old.Else the past site is retained in memory.If cannot be improved, its counter holding the number of experiments is increasing by 1, else, the counter is reset to 0.
An onlooker bee assess the nectar information taken from all employed bees and chooses a location for the food source with a probability regarding to its nectar quantity.This probabilistic choice depends on the fitness values of solutions in the population.A fitness-based choice scheme might be a roulette wheel, stochastic universal sampling, ranking based, tournament choice or another choice scheme.In basic ABC, roulette wheel choice system in which each slice is commensurate in size to the fitness value.The probability can be expressed as follows: In this probabilistic choice scheme, as the nectar quantity of food sources is increased, the number of onlookers which visits them also increase.In the ABC algorithm, a real random number is created within the range [0,1] for each source.If the probability value ( ) in equation ( 15) related with that source is bigger than this random number, then the onlooker bee produces an adjustment on the site of this food source position by using equation (13) as in the case of the employed bee.After the source is assessed, the greedy choice is applied and the onlooker bee either saves the new site by forgetting the old, or retains the old one.If solution cannot be improved, its counter holding experiments is increased by 1; else, the counter is reset to 0. This process is recurrent until all onlookers are distributed onto food source positions [27].

Proposed algorithms
In the proposed algorithms, an optimization technique of PSO and ABC are used to assist in determining the optimal placement of meters for power system state estimation.These algorithms are randomly looking for the best location of meters based on the minimum error in the state estimate.The major concern is to realize a high accuracy level for state variables from the optimal meters placement obtained.Compared with conventional methods, PSO and ABC are capable to search the optimal placement of meters without having to test possible location one after another since PSO and ABC are an optimization methods.It searches better location of meters by iteratively improving the random location guided by selected minimum objective function.

Optimal placement algorithm of meters by using PSO
Step1: Inputting the voltage of reference bus, traditional and real data of measurements.The real measurements taken from Newton-Raphson load flow.
Step2: Initializing the parameters of PSO.Setting up the group of the parameters of the PSO such as, acceleration constants ( and ), number of individual(Number of variables ( ) ), maximum number of iteration, maximum and minimum of Inertia weight ( ) and Population size .
Step3: Calculating the state estimation by using the traditional method (WLS).
Step4: Randomly creating an initial population of individuals (locations of meter) , the velocities and the positions of the individuals.Setting the iteration index i .
Step5: For each individual (location of meter), if the number of the bus is within boundary limits, the state estimator is calculated using WLS method.Otherwise, that individual (location of meter) is not feasible.
Step6: Recording and updating the optimum values.The two optimum values are stored in the process of the search.Each individual moves in the direction related to its previously optimum solution it has reached so far which is stored as .Another optimum value to be stored is the , which accounts for the global optimum value achieved by neighboring individuals.and are the minimal value of the cost function.This step also updates and .Initially, the fitness of each individual is compared with its .If the current solution is better than its , then is replaced by the current solution.Then, the fitness of any particle is compared with .If the fitness of any individual is better than , then is replaced.Step7: The position and the velocity of the individual have to be updating.This is done by using equation (9).A movement in the direction of chosen bus is represented by the velocity of an individual.Meanwhile, the position of the individuals is updated by applying Equation (11).
Step8: Checking End criterion.The end criterion is checked, if it is satisfied, the algorithm is stopped; otherwise, step 3-7 is repeated until the end criterion is satisfied.In this paper, the particles are locations of meters as shown below: , - where, : the number of meter with selected bus, which limits according to number of existing measurements and : location of meter.The Fitness Function (objective function) In this paper, PSO and ABC are implemented to find the optimal locations of meters through minimizing the error in bad measurements data, where the optimal solution is found by minimizing the objective function in equation ( 17) through exchanging the location of meters between the real and traditional measurements.The process will be finished when the termination condition reaches a prescribed value.Figure (1) and (2) shows the procedure of PSO and ABC techniques.Tables (1) and (2) illustrates parameters of techniques used.
, -, -, - Where, , -: Residue of measurement errors , -: is a diagonal matrix whose elements are the variances of the measurement error The termination condition : maximum number of iteration.

Optimal placement algorithm of meters by using ABC
Step1: Inputting slack bus voltage, traditional and real measurement data.The real measurement taken from Newton-Raphson load flow.
Step2: Initializing the population of the colony(location of meters).Randomly, the Scout bee selects the food source (location of meters) within the boundaries.A food source positions(location of meters) are initialized through the scout bees which is indicated as , where the value of is bounded within 1 to nPop.
Step3: The employee bee assesses the food sources (location of meters) for its fitness value(cost function) and the best location of meters are kept as global minimum (minimized objective value).To check the better food source(optimum location of meters),the employee bee visits the neighborhood(another buses).If the objective function(fitness value) for the recently visited food source is better than previous one substitute previous food source by new one; otherwise, the previous one is kept.

Step4:
The employee bee share their information related to the nectar amounts and the positions of their sources(location of meters) with the onlooker bees on the dance area.The onlooker bee assesses the probability of the food sources (location of meters) by using equation (15) and modifies the position of the food source.Based on the information that share more onlooker bees were sent to high fitness food source and less onlooker bees sent to small fitness food source.
Step5: Food sources (location of meters) which cannot be enhanced after a period of time are abandoned and the scout bee creates new food sources (new location of meters).Equation ( 13) is used to create an adjacent food source.
Step6: Repeating the process until the termination condition is reached.

Results and Discussion
The algorithms are examined and tested on IEEE-14, IEEE-30 bus standard test system.The Mean Square Error (MSE) is used as index to illustrate the accuracy of the proposed algorithms.MSE is defined in equation ( 18) as follows: Where, N: number value of measurement.: true value of measurement .: estimated value of measurement .The proposed algorithms for optimal placement of meters by using artificial intelligence technique PSO and ABC are applied on IEEE-14 ,IEEE-30 bus standard systems .The optimum placement of meters obtained for IEEE-14 and 30 bus system are given in Table (3) and Table( 4) respectively.

IEEE-14 bus
The proposed algorithms are applied to determine the best estimate vector of IEEE-14 bus test system with a set of 20 conventional meters [28].Which includes optimal placement of meters by using PSO and ABC based on weighted least squares and rectangular coordinates system to avoid the singularity of gain matrix.A comparison was made in terms of accuracy and results.The objective function randomly searches the best possible meters placement of the system which produces the best quality of the state variable( ).As many researchers indicated that the weight of meters has an effect on results and accuracy for power system state estimations.The results obtained reveal that the accuracy of estimated state is increased as a measurement placements are exchanged throughout minimizing the errors in measurements.
The results of applying the proposed algorithms to the IEEE-14 bus test system are given in Tables (5 and 6) and Figures( 3 and 4).There is a clear discrepancy between the true bus bar voltages and the estimated voltages obtained by using traditional WLS, while the estimated voltages vector obtained by using the proposed algorithms are similar to the true voltages.It can be seen that the accuracy of proposed methods related with a new optimal placement of meters are better as compared with conventional method (WLS).From table (9) it can be seen that MSE for voltage estimates for PSO (9*10^-6) and ABC (5*10^-6).Also from table (10) it can be seen that MSE for bus angle for PSO (4*10^-6) and ABC (5*10^-7).This shows that ABC method is better than PSO.Number of iteration for PSO (6 iter.) is better than ABC (7 iter.) and both them are less than WLS (8 iter.).On the other hand, the execution time for proposed methods are less than WLS and that shown in table (11).

Table 3.Optimal Placement of Meters by using PSO and ABC for IEEE-14 bus
The optimal placement of meters by using PSO for IEEE-14 bus standard system The optimal placement of meters by using ABC for IEEE-14 bus

IEEE-30 bus system
The set of measurement of the IEEE-30 bus system consists 46 conventional meters [28].Tables (7 and 8) and Figures (5 and 6) show the results obtained by the application of the proposed algorithms to the IEEE-30 bus test system.There is a similarity between the estimated state vector obtained by using the proposed algorithms and the true values.Also, it is clear that a better accuracy is achieved with using the optimal placement algorithms as compared with the conventional method (WLS).
A comparison of the MSE for the elements (voltage estimates and bus angle) of the estimated vector for both artificial technique PSO and ABC clarify the effectiveness of the proposed algorithms.From table (9) it can be seen that MSE for voltage estimates for PSO (3.8*10^-4) and ABC (3.3*10^-5).Also from table (10) it can be seen that MSE for bus angle for PSO (2*10^-5) and ABC (3*10^-6).This shows that ABC method is better than PSO.Number of iteration for PSO and ABC (9 iter.) are less than WLS (12 iter.).on the other hand, the execution time for proposed methods are less than WLS and that shown in table (11).

Conclusion
The application of swarm artificial intelligence technique in the selection the optimal location of the meters has been presented.Two algorithms have been implemented.The algorithms utilized PSO and ABC technique for obtaining the optimal placement.The application of the proposed algorithms on typical test systems has been given in the paper.The results obtained reveal the importance of the meter locations in estimating the state vector of the system in terms of the execution time, accuracy and the number of iterations for the system to be converged.The results also reveal that the ABC technique is more efficient than the PSO technique in the estimation of the system state.

Figure 4 .
Figure 4.Comparison between actual and estimated values of the bus phase angle

Figure 5 .
Figure 5.Comparison between actual and estimated values of the bus voltage magnitude

Table 1 .
Parameter of PSO for Optimal Location of Meters

Table 2 .
Parameter of ABC for Optimal Location of Meters

Table 4 .
Optimal Placement of Meters by using PSO and ABC for IEEE-30 bus

Table 5 .
Actual voltages, estimated voltage, and errors for the 14-Bus system Figure 3.Comparison Between Actual and Estimated Values of the Bus Voltage Magnitude

Table 6 .
Actual voltage angles, estimated angles, and errors for the 14-Bus system

Table 7 .
Actual voltages, estimated voltage, and errors for the 30-Bus system

Table 8 .
Actual voltage angles, estimated angles, and errors for the 30-Bus system Figure 6.Comparison between actual and estimated values of the bus phase angle

Table 9 .
Comparison of the estimation accuracy in bus voltage magnitude

Table 10 .
Comparison of the estimation accuracy in bus phase angle

Table 11 .
Execution time in seconds